The best thing about this gun is that it is cheap and can be purchased without having to upgrade your contract.
Great for beginners until you are able to purchase a Shotgun.

The best gun in the game.
In skilled hands, it does the same if not more DPS than the Supernova in real combat conditions.
The damage dropoff of the Shotgun is never really a factor, as being close to enemies doesn't really matter if you can just dodge their attacks with the dash, and some even punish you for being far away such as the Nightwalker's leap ability which is hard to dodge.

The DPS of the Supernova is subject to RNG since it is random how many explosions you get and how fast you set the enemy on fire. It can be as bad as the regular Pulse Rifle if you get bad RNG, or slightly better than the Shotgun if you get good RNG, however this is raw DPS and doesn't take into account needing to dodge enemy attacks.

This is more of a tool than a weapon. You should only be using this on things that only take heat or fire damage, such as Lurk Roots and Slimes. It cannot compare to the other ranged weapons in regular combat.
However, it can still be useful in regular combat! Try combining it with a gun, by lighting the enemy on fire for extra DPS, then switching to a gun to shoot them while they're on fire.
Not only will the enemy be taking damage over time from the fire, but it also causes them to take more damage from your gun! As of v0.4.0.0, enemies that are on fire take 20% increased damage.

Outright worse than ranged weapons. The Tier 3 Knife, Shovel and Pickaxe deal more DPS than the Pulse Rifle, but less than the Shotgun and Supernova. The lower Tier versions are even worse. Unlike guns, they also require you to consistently be in melee range and require you to dodge more often, reducing the DPS.
If you REALLY want to use a melee weapon, the Knife is overall the best. It's the utility tool you will end up using the most on average (more than the Pickaxe and Shovel) because of the existence of Lurk Roots on Tier 2 and 3. Additionally, it has the highest DPS, tied with the Shovel. The Pickaxe has slightly less DPS out of all three melee weapons.

In this video, the Supernova with good RNG only has slightly better DPS than the Shotgun.
In real combat against enemies where dps actually matters (Night Walkers etc.), you will be dodging attacks with your dash, which will make the DPS of the rifles suffer because it is hard to dodge and perfectly shoot to prevent overheat and perfectly time when to start shooting again when the heat meter is empty. Whereas, the DPS of the Shotgun hardly suffers because of its burst-damage, it's easy to use while dodging without jeopardizing DPS.

Additionally, the Shotgun here isn't even doing its maximum DPS, because I am standing at a realistic distance away. So it can actually do even more damage if you get closer.
Melee weapons are not included in this video because there is just no competition, ranged weapons are better.